In medical devices for extracorporeal blood treatment (Dialysis), peristaltic pumps are often used which supply the blood removed from the patient to a dialyzer and return the blood to the patient. Such pumps operate peristaltically, wherein a tube segment in the form of a loop lies on a correspondingly curved running surface. In that case, a pump's rotor lying inside the running surface moves with its outer edges along the tube segment, whereby it presses locally on the tube and thus, together with the elastic material properties of the tube segment, it allows a blood supply through the tube segment. Therefore the blood is introduced into the tube segment via a first connection and conducted away via a further connection at the other end of the tube segment. Thus for example the tube segment forms, together with the supply and discharge lines and the plurality of air traps, a so-called transfer system, with which the blood of the patient is supplied to a dialyzer and then supplied back to the patient.